A new non-local Hartree-Fock approach to the embedding of a single impurity (atom, ion or molecule) into a solid is proposed. The method, which is based on both a coupled Hartree-Fock calculational scheme and the Green function embedding method of Inglesfield, aims at calculating lifetimes of the electronic states of the embedded impurity, either in its ground or an excited state. As an example, the author presents an application of this method to the embedding of a Li and a He atom into a metallic jellium.